Transcript Metaphysics of Emergence

Metaphysics of Emergence
Rainer E. Zimmermann
[email protected]
Research Programme
• Language & Space
• Theory of Spaces, Networks, Systems
• Systematical Line: Spinoza – Schelling –
Bloch (Modern Dialectical Materialism)
• Methodological Line: Ontological Triad
(Cognition, Communication, Cooperation)
& Epistemological Triad (Spaces,
Networks, Systems)
Confrontational Idea
• Emergence vs. Evolution
• Example: Cell Membranes
• David Deamer et al. (2002): The First Cell
Membranes. Astrobiology 2 (4), 371-381.
Co-operation
• Thanks go in particular to José María Díaz
Nafría (León), Klaus Fuchs-Kittowski
(Berlin), Iain Hamilton Grant (Bristol),
Wolfgang Hofkirchner (Vienna), Peter
Knopp (Berlin), Jason Wirth (Seattle).
Recent Literature
• Gilles Châtelet: L’enchantement du virtuel. Ed.
Charles Alunni, Cathérine Paoletti, Rue d’Ulm
(ENS), Paris, 2010.
• Louis H. Kauffman: Eigenforms and Quantum
Physics (at the Foerster 100th birthday jubilee, U
Vienna 2011)
• Richard Healey: Gauging What’s Real. Oxford
University Press, 2010
• John Baez, Javier P. Muniain: Gauge Fields,
Knots, and Gravity. World Scientific, 1994.
Preliminary Remarks
• The Concept of Motion (Epistemological
rather than Ontological)
• Hence: Evolutionary Systems are models
of the wordly substratum (Matter: Urstoff =
Arist. hypokeimenon), not models of
substance (ousía) as the world‘s ground.
• Metaphysical difference: worldly
categories vs. conditions of substance
Preliminary Remarks
•
•
•
•
•
•
•
•
(Modern) Attributes of Substance:
energy-matter vs. information-structure
http://www.mdpi.com/2078-2489/3/3/472
New Ethics Proved in Geometrical Order: Spinozist
Reflexions on Evolutionary Systems
(Emergent Publications (Az.), 2010).
Nothingness as Ground, and Nothing but Ground
(Northwestern University Press, forthcoming 2013)
[with Simon M. Wiedemann] Kreativität und Form
(Glasperlenspiel) (Springer, 2012)
Emergence
• Every resultant is clearly traceable in its
components, because these are homogeneous
and commensurable. It is otherwise with
emergents, when, instead of adding measurable
motion to measurable motion, or things of one
kind to other individuals of their kind, there is a
co-operation of things of unlike kinds. The
emergent is unlike its components insofar as
these are incommensurable, and it cannot be
reduced to their sum or their difference. (Lewes
1875)
Emergence
• (1) radical novelty (features not previously
observed in systems);
• (2) coherence or correlation (meaning integrated
wholes that maintain themselves over some
period of time); structural stability, interaction of
micro- and macro-levels (upward&downward
causation (supervenience), top-down&bottomup);
• (3) product of a dynamical process (it evolves).
Emergence
Continuous Models (Keller/Segel; Prigogine)
(Selbstreferenz & poetische Praxis, 1991)
(a, ): amoebae/acrasine density
a/t = –  (D1) +  (D2a),
/t = – k1 + k-1c + a f() + D 2
k: rate constants for acrasin-acrasinase reactions, eqns. for
c and  skipped (complex building)
Emergence
Slime Mold Aggregation (Dictyostellum discoideum)
Emergence
• Matrix representation of operator
formulation:
• E11 = –  (D1), E12 =  (D2) – /t,
• E21 = p() + D 2 – /t, E22 = f(),
• E x = 0. (x = (,a))
Emergence
• E  E* = N(E) Negation Operator
(Negator)
• Instability (Onset of Aggregation) requires
new structural stability! Hence:
• E*  E** = N(E*) = NN(E) = N2(E)
• Negation of the Negation
• If E = N0(E), then the following diagram is
consistent:
Emergence
• 1 (structurally stable state)  N(E)  2 (unstable state)
•


•
N2(E)
•

•
4
 …  3 (stable again)
• Sandwich structures: Schelling (PP)! The potential must be loaded
with concrete power in order to become actualized. (Transition from
micro to macro levels!)
• Metaphysical perspective: Nothingness that is loaded with power
becomes non-being. Non-being that is actualized becomes Being.
Interlude: Systemic Perspective
1. Network: Dynamical Core of Interactions
(Transport of Information  software)
2. Space: Mean Free Path of Interactions
(Domain of Influence 
software/hardware)
3. System: Boundary Operator as defining
the region of interaction with the
environment (software/hardware)
Interlude: Systemic Perspective
• However: These categories are actually absent
in absolute terms. They are simply technical
ordering principles so as to make modeling
possible at all.
• The systemic perspective is nothing but
epistemological.
• But for human beings, the epistemology is also
ontological. (Sandkühler, HHHolz)
• Hence: The onto-epistemic result is useful after
all. It adequately maps the relationship between
cognition and communication – but not the world
as it really is!
Emergence
• Short Excursion into Topoi
• Essentially, a topos is a category plus an
additional structure including initial and
terminal objects, push-outs and pull-backs
such that the following diagram commutes:
Emergence
• 1. Category
• A category C is a class of objects ob(C) and a class of
morphisms mor(C) such that each morphism has a
unique source and target object, respectively. Also, for
every three objects a, b, c there is a binary operation of
the form mor(a, b) x mor(b, c)  mor(a, c) called
composition such that associativity and left and right
identity laws are valid.
• 2. Additional Structure …
Emergence
Emergence
• Generic Conjectures:
• NEG is the category of negators with the objects being
the structurally stable world states and the morphisms
being the negators themselves.
• Conjecture 1: NEG is a topos.
• GAME is the category of games with the objects being
positions of agents in their utility space and the
morphisms being the strategies of agents.
• Conjecture 2: NEG and GAME are generically
isomorphic.
• (Because essentially, strategies act as negators among
agents or their positions, respectively.)
Emergence
• Continuous scheme:
• o = coefficient, x = differential operation
• ox + ox + … + ox = 0,
• …
…,
• ox + ox + … + ox = 0.
Sleeping variables: their o = 0. (the x are actually
there)
Field of possibilities: their x = 0. (the x may come
later)
Emergence
• Differential operators relatively simple
case, but useful entry
• From physical structures to microorganisms and to populations in biology
similar approaches
• Most complex but best-known everyday
example of emergence:
Emergence
Emergence
Emergence
• Note that both these states are stable,
hence they can only be states 1 and 3 of
the appropriate sandwich structure.
• In other words: The child must be the
negation of the negation of the adults.
• Only strict case of individuality! (different
from other animals)
Emergence
Emergence
• Analysis of necessary and sufficient
conditions.
• Aristotelian: enérgeia/entelecheia
(actuality) vs. possibility
• possibility: katà tò dynatón vs. dynámei ón
• (being according to possibility („I‘ll do my
best“)/being in possibility: the potential to
become something)
Emergence
• concepts
• 1. thinkability in logical sense
• 2. adequacy with respect to formal experience
(in the epistemic sense)
• 3. relationship between possibility and actuality
(in the metaphysical sense)
• types
• 1. what is not yet
• 2. what is contingent
• 3. what is included in the necessary
Emergence
• Bloch‘s Aristotelian interpretation:
• „Actualizing is thus to activate subjective
potential in order to produce consequences of
the objectively-real possible.“ (EM 255; my
translation)
• (Aristotle, Physics, 201b.3-5): „The becoming
actualized of what is possible in so far as it is
possible [of the being in possibility], this is
obviously motion.“ (… he tou dynatou, he
dynatón, entelécheia phaneròn óti kínesis estin.)
Emergence
• Cusanus: God is everything in complicated
manner (omnia complicite);
• Hence: It is necessary to unfold what is
folded (explicari in mundo)
Emergence
• Shifts of Possibility (Bloch)
• 1. the formally possible (that can be thought)
• 2. the matter-of-fact objectively possible (that can be:
problematic judgement)
• 3. the possible according to matter and object (that can
become, independent of its knowledge)
• active can be (power: Vermögen) vs. passive can
become (potentiality)[subjective vs. objective factor:
open power vs. Open potentiality]
• 4. the objectively real possible (the substratum =
matter/dynámei ón/Urstoff)
Emergence
• Social, psychological, biological (chemical
as well as physical) factors shape the field
of possibilities.
Emergence
• Rosetta stone of universal isomorphisms
(conjecture)
• NEG  OPS  …  GAME  SOCS
• Emergence shows up in terms of initial and
terminal objects. (0  A, a: 1  A)
• An element of a set A is any mapping whose
codomain is A and whose domain is 1.
Emergence
• particle annihilation & creation
• n = ( n!)-1/2 (a†)n n
• an = n n – 1
• a†n = (1 n) n + 1
• a0 = 0
• k = ak†0
Emergence
• From Quantum Gravity to the DNA (Lou
Kauffman)
• Temperley-Lieb algebra/Artin braid group/Jones
polynomial of invariants of knots and links
• creation operator cup := a†: C  V  V
• annihilation operator cap := <a: V  V  C in
order to define the computation of a link
amplitude (state sum) of type:
• Z = <cupMcap
Emergence
• Motivation:
•

•

+=

in t/x co-ordinates
Emergence
• Categorification of Quantum Physics
• Jeffrey C. Morton, Jamie Vicary: The
Categorified Heisenberg Algebra I: A
Combinatorial Representation.
• http://arxiv.org/pdf/1207.2054v1.pdf
Emergence
• A. Kock, G. E. Reyes: Fractional Exponent
Functors and Categories of Differential
Equations. (1998)
• http://home.imf.au.dk/kock/ODE55.pdf